1) PARTLY FIXED Were added two console commands to hide top HUD and bottom HUD in patch March 16, 2017
Please, add console command to hide Items pickups, Fight recap and Stats dropdown.
No single HUD console command currently is working in live games and replays, examples:dota_fight_recap_disable 1 — disabling fight recap
dota_sf_hud_stats_dropdown 0 — hide heroes stats dropdown
dota_show_itempickups 0 — hide itempickups/stolen skills/Roshan timer
It's also impossible to hide different parts of HUD: map, heroes picked, inventory. You can toggle only full HUD and only in replays (not in live games) with this command hud_toggle_visibility 0
Looks like most, if not all _sf_ commands don't work since those were scaleform-specific, and have not been ported to the new interface.

CORRECTIONS:dota_show_itempickups 0 does work! I guess gl / vulkan are different and if you use those renders you need to also use dota_show_itempickupssf 0

stat_dropdown close (or none or 0) is an alternative to the old sf_ function. It's actually the proper one to use.
You can also select a specific one ( stat_dropdown networth ). Choices are kda lasthits_denies level xp_per_min gold gold_per_min totalgold networth buyback.
Or cycle them ( stat_dropdown_cycle ) or sort them ( stat_dropdown_sort ).

hud_toggle_visibility works fine in live spectated games (it would be stupid to also allow it for your actual matchmaking games). If it does not for you, enter sv_cheats 1 into console.